Before installing WoW Patch 5.0.4 I had no problems.
After installing I am unable to pin both launchers. When I pin one (say the WoW launcher) and right click on the other (Diablo 3 launcher) I don't see the Pin to Taskbar option. I do see the Unpin from Taskbar option and when I click that (remember I'm on the Diablo 3 right-click menu), it unpins the WoW launcher. It happens vice-versa as well.
Same thing happens when pinning to Start Menu.